Question

Simplify each expression for the perimeter of the deck

Answer 1

1) Perimeter: $(d+d+d+d)+(5+5+5+5)$

2) Perimeter: $4(d+5)$

3) The two expressions are the same

Step-by-step explanation:

1)

The figure of the problem is missing: find it in attachment.

Here we know that the deck has a squared shape, and the size of each side is

$L=d+5$

The perimeter of a figure is equal to the sum of the lengths of all the sides, therefore for this square:

$p=L+L+L+L=(d+5)+(d+5)+(d+5)+(d+5)$

Here we want to rewrite the perimeter as an equivalent expression by grouping the like terms, therefore by grouping the terms with $d$ and the terms with $5$. Doing so, we get:

$p=d+5+d+5+d+5+d+5=(d+d+d+d)+(5+5+5+5)$

2)

In this case, we want to find the perimeter of the deck by multiplying the number of sides by the length of one side.

For the squared deck in this problem, we have:

n = 4 (number of sides)

$L=d+5$ (length of a side)

Therefore, by multiplying the two factors, we can write the perimeter as

$p=n\cdot L = 4 \cdot (d+5) = 4(d+5)$

3)

Now we can simplify each expression for the perimeter of the deck.

For expression 1, we had:

$p=(d+d+d+d)+(5+5+5+5)$

Simplifying, we get:

$p=(d+d+d+d)+(5+5+5+5)=(4d)+(20)=4d+20$

For expression 2, we had

$p=4(d+5)$

We can simplify this by using the distributive property, so we get

$p=4\cdot d + 4\cdot 5 = 4d+5$

And we notice that the two expressions are identical.

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